International Journal of Trend in Scientific
Research and Development (IJTSRD)
International Open Access Journal
ISSN No: 2456 - 6470 | www.ijtsrd.com | Volume - 2 | Issue – 4
Effect of Load variation and thickness
on deflection and operating stress of wave spring
Hardik C. Tekwani, Dhruv D. Joshi
Assistant Professor, Mechanical En
Engineering Department,
Vadodara Institute of Engineering
Engineering, Gujarat, India
ABSTRACT
Wave springs are used for load bearing into
assemblies. When force applied to the spring, load is
gradual or abrupt. Typically wave spring will occupy
an extremely small space after compressions. In this
paper effect of change in thickness of wave spring oon
the deflection of spring and on operating stress is
studied. This study leads towards the impact of
thickness change under different load condition. The
result reveals that after increasing the thickness from
0.1181 to 0.23622 inch, drastically decrement noticed
in the deflection as well as operating stress for
different loading condition in wave spring. Study
shows the deflection for two different spring materials
(nickel and beryllium copper) considering different
parameters that help to choose best spring
ing material.
Keywords: wave spring thickness, Deflection, working
stress, Load on wave spring, etc.
1. INTRODUCTION
Spring is made up of elastic material as after getting
compressed it stored the energy. Generally springs are
made of steel. The spring constant of a spring can be
defined as the change in the force it exerts, divided by
the change in deflection, so spring rate is described by
unit N/m. in case of torsion spring, when it is twisted
about its axis by an angle, it produces a torque
proportional
nal to the angle and spring's rate having unit
Nm/rad. wave springs replaced helical springs
because wave springs required less height compare to
coil spring for the similar load application. Wave
springs were first discovered by Smalley industries of
USA in 1990’s. They manufacture wave spring of
many types. Small springs can be wound from pre
pre-
hardened stock, while larger ones are made from
annealed steel and hardened after fabrication. Some
non-ferrous
ferrous metals are also used including phosphor
bronze and titanium for parts requiring corrosion
resistance and beryllium copper for springs carrying
electrical current. Common spring materials include
stainless steel, alloy steels, carbon steels, non-ferrous
non
materials and some super-alloys
alloys which exist in the
market
ket
with
preparatory
designations
and
nomenclature. Each spring material has diverse
compositions, individual properties and also for a
particular type of spring, more than one feasible
alternative spring materials may be available in the
market.
1.1
Wave spring:
Among the many types of springs, wave springs have
attracted considerable attention this kind of long and
reliable source of long lasting durability and
considerable effectiveness than rest of the springs.
Wave springs are used to reduce the height of the
spring and to produce the same end effect end that of
a coil spring. Wave springs operate as load bearing
devices. They take up play and compensate for
dimensional variations within assemblies. A virtually
unlimited range of forces can be produced whereby
whe
loads build either gradually or abruptly to reach a
predetermined working height. This establishes a
precise spring rate in which load is proportional to
deflection. Functional requirements are necessary for
both dynamic and static spring applications.
applications Special
performance characteristics are individually built into
each spring to satisfy a variety of precise operating
conditions. Typically, a wave spring will occupy an
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 4 | May-Jun
Jun 2018
Page: 684
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
extremely small area for the amount of work it
performs. The use of this product is demanded, but
not limited to tight axial and radial space constraints.
1.2 Wave spring types:
Gap type wave spring has gap between two ends.
Continued deflection causes the gap ends to move
closer together while the outer dia. presses against the
bore [fig. 1(a)]. Overlap type has overlapping ends
and ends are free to move circumferentially during
compression [fig. 1(b)]. Crest-to-Crest wave spring
has more numbers of turn. No need to use key
between springs because the spring is integrally
1.3 Spring materials and their properties:
For manufacturing of spring the material is selected
by considering many parameters like spring is made
of a material which having elasticity for storage of
energy after compression, higher yield strength, etc.
Also material must be compatible with the
environment and withstand effects of temperature and
formed. Crest springs replaced helical spring because
crest springs can develop similar forces so occupy less
the axial space and solid height [fig. 1(c)]. Nested
Wave Springs are pre-stacked in parallel from one
continuous filament of flat wire used for higher load.
Nested springs result in a spring rate that increases
proportionally to the number of turns [fig. 1(d)].
Wavo wave spring has round-section and used for
high load application and give accurate spring rate
[fig. 1(e)]. In linear wave spring forces act linearly or
radially depending on the installed position and axial
pressure is obtained by laying the spring flat in a
straight line [fig. 1(f)].
corrosion without an excessive loss in performance
because corrosion and temperature decrease spring
reliability. Engineer must analyze about the
compression rate of the spring and tensile strength for
fatigue frailer and life cycle of the spring. According
to the requirements of the material different materials
with their properties are shown in table 1.
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Page: 685
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
Table 1 spring material properties [6]
Density
(gm/cc)
Tensile Modulus
Strengt of
h (MPa) Elasticity
(GPa)
Design
Stress
percentage
Min.
Tensile (%)
Max.
Operatin
g Temp
(˚C)
Rockwe
ll
Hardne
ss
(HRC)
Materi
al Cost
($/Kg.)
High Carbon Steel (ASTM 7.85
A 228)
2168.5
207
45
121
50.5
35
Beryllium Copper
(ASTM B 197)
Alloy 8.26
1310
128
45
204
38.5
33
8.44
1241
179
40
288
29
55
Chrome Silicon Alloy Steel 7.85
(ASTM A 401)
1844.5
207
45
245
51.5
30
Stainless Steel (AISI 304)
7.92
1551.5
193
35
288
40
15
Inconel 600
8.47
1379
214
40
371
40
45
Nickel Alloy(ASTM A 286)
7.92
1241
200
35
510
38.5
32
Material
Monel K500
2. CALCULATION
Table 2 value of K corresponding to N [7]
Deflection = f =
. .
. .
N
2.0
4.0
- 4.5
6.5
K
3.88
2.9
-
7.0-9.5
10.0+
2.3
2.13
Operating stress = S =
P = Load (lb.)
b = Radial Wall, in. [(O.D. - I.D.) ÷ 2]
L = Length, overall Linear (in.)
K = Multiple Wave Factor
t = Thickness of Material (in.)
H = Free height (in.)
I.D. = Inside Diameter (in.)
N = Number of Waves (per turn)
W.H. = Work Height (in.) [H-f]
O.D. = Outside Diameter (in.)
E1 = Modulus of Elasticity (psi) of E2 = Modulus of Elasticity (psi) of
Beryllium Copper Alloy (ASTM B
Nickel Alloy(ASTM A 286)
197)
Dm = Mean Diameter, in. [(O.D. + S1 = Operating Stress (psi) of Nickel S2 = Operating Stress (psi) of
Beryllium Copper Alloy (ASTM B
I.D.) ÷ 2]
Alloy(ASTM A 286)
197)
Z = Number of Turns
F1 = Deflection (in.)
Alloy(ASTM A 286)
of
Nickel F2 = Deflection (in.) of Beryllium
Copper Alloy (ASTM B 197)
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 4 | May-Jun 2018
Page: 686
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
2456
Table 3 calculation of operating stress and deflection @ 600lbs
P
K
ID
OD
Dm
Z
b
t
N
E1
E2
S1 = S2
F1
F2
600
3.88
3.937
4.7244
4.3307
20
0.3937
0.1181
2.5
29007548
18564830
178391.8019
4.288643
6.701004947
600
3.88
3.937
4.7244
4.3307
20
0.3937
0.2362
2.5
29007548
18564830
44597.95048
0.536080
0.837625032
600
3.88
3.937
4.7244
4.3307
20
0.3937
0.3543
2.5
29007548
18564830
19821.31132
0.158838
0.248184384
600
3.88
3.937
4.7244
4.3307
20
0.3937
0.4727
2.5
29007548
18564830
11149.48762
0.067010
0.104703129
Deflection (Nickel v/s Beryllium copper)
8
7
6
5
Nickel
4
Beryllium
Copper
3
2
1
0
0.1181
0.2362
0.3543
0.4727
Table 4 calculation of operating stress and deflection for 1000lbs
P
K
ID
OD
Dm
Z
b
t
N
E1
E2
S1 = S2
F1
F2
1000
3.88
3.937
4.7244
4.3307
20
0.3937
0.1181
2.5
29007548
18564830
297319.6698
7.147737916
11.16834093
1000
3.88
3.937
4.7244
4.3307
20
0.3937
0.2362
2.5
29007548
18564830
74329.91745
0.893467239
1.396042615
1000
3.88
3.937
4.7244
4.3307
20
0.3937
0.3543
2.5
29007548
18564830
33035.51887
0.264731033
0.413642255
1000
3.88
3.937
4.7244
4.3307
20
0.3937
0.4727
2.5
29007548
18564830
18582.47936
0.111683404
0.174505325
Deflection (Nickel v/s Beryllium copper)
12
10
8
Nickel
6
Beryllium
Copper
4
2
0
0.1181
0.2362
0.3543
0.4727
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International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
2456
2.1 Comparison of deflection for 600 lbs and 1000 lbs load on the wave spring of nickel & Beryllium
copper
12
10
8
F1 @ 600 lbs
6
F2 @ 600 lbs
F1 @ 1000 lbs
4
F2 @ 1000 lbs
F2 @ 1000 lbs
F1 @ 1000 lbs
F2 @ 600 lbs
2
0
0.1181
0.2362
F1 @ 600 lbs
0.3543
0.4727
2.2 Comparison of operating stress for 600 lbs and 1000 lbs load on the wave spring
350000
300000
250000
200000
150000
100000
50000
0
0.1181
0.2362
0.3543
0.4727
Operating stress for 600lbs
Operating stress for 1000lbs
3. CONCLUSION


For the wave spring calculation conclude that as
the wave increase the frequency of the spring will
decrease and also chart shows the frequency
versus wave of spring for two different load. Here
rapid decrement of frequency from 1000lbs to 600
lbs.

For nickel and beryllium copper wave spring, the
result shows that the deflection occur at maximum
level in the case beryllium copper having
havi value
11.16834093 on load of 1000 lbs

For better properties metal matrix composite can
be preferred for the future scope.
For the helical spring,
ng, frequency versus no. of
active coil chart shows that as the no. of active
coil decrease frequency also decrease.
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International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
REFERENCES
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analysis of a shock absorber, International Journal
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Issue 4, pp. 578-592
3. Youli Zhu *, Yanli Wang, Yuanlin Huang. Failure
analysis of a helical compression spring for a
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4. Animesh das and Awinash kumar, “Selection of
Spring Material Using PROMETHEE Method”
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5.
Puvvala Raju and Mrs.N .Venkata Lakshmi
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spring” International journal of advance research
and innovative ideas in education vol. 4 Issue 2.
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